Intersecting chords method in minimum zone evaluation of sphericity deviation

Minimum zone evaluation of sphericity deviation is a very important and complex problem in precision measurement technology. For the evaluation of sphere form deviation in Cartesian coordinates, a new minimum zone evaluation method of sphericity deviation using the relationship of intersecting chords is introduced. First, the measurement models of sphericity deviation in Cartesian coordinates are constructed and a calculation method based on general quadratic surface theory is presented for obtaining least square center. Then, according to the classification of minimum zone sphericity deviation models, using the intersecting chord method to build the 2+3 and the 3+2 models of minimum zone evaluation of sphericity deviation. Finally, through the intersecting chord geometry model produces virtual center so as to accurately determine the maximum chord and the maximum section of evaluation model, meanwhile, the purpose of fast and accurate constructing model is also achieved. The results and examples indicate that intersecting chord method has high the computational efficiency and the accuracy of evaluation. In addition, the method has little influence on the measurement space from the measurement coordinate system and the geometry form error, which significantly improves the minimum zone evaluation of sphericity deviation.